Filters that have been used in prior timing recovery circuits, automatic gain control circuits or the like, retained some memory of the past timing or gain error estimates. Such prior filters inevitably slow down the tracking of the timing or gain, or have so broad a band width as to allow the recovered timing (gain) to have considerable jitter. Indeed, in order to recover timing and the like from data signals with very low signal-to noise-ratio (SNR) it is necessary to do some narrow band filtering. This narrow band filtering is in conflict with a fast acquisition time. Attempts at overcoming these problems, typically employed a filter that used a so-called "gearshift" which after some initial start-up interval shifted the filter time constant from short, fast and noisy to long, slow and quiet. Use of such gearshift filters is undesirable because a significantly long time is required before the time constant shift is effected. Consequently, fast acquisition was compromised.